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Microscopic Description of Insulator-Metal Transition in High- Pressure Oxygen Received: 25 April 2016 Luis Craco1, Mukul S

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Microscopic Description of Insulator-Metal Transition in High- Pressure Oxygen Received: 25 April 2016 Luis Craco1, Mukul S www.nature.com/scientificreports OPEN Microscopic description of insulator-metal transition in high- pressure oxygen Received: 25 April 2016 Luis Craco1, Mukul S. Laad2 & Stefano Leoni3 Accepted: 19 April 2017 Unusual metallic states involving breakdown of the standard Fermi-liquid picture of long-lived Published: xx xx xxxx quasiparticles in well-defined band states emerge at low temperatures near correlation-driven Mott transitions. Prominent examples are ill-understood metallic states in d- and f-band compounds near Mott-like transitions. Finding of superconductivity in solid O2 on the border of an insulator-metal transition at high pressures close to 96 GPa is thus truly remarkable. Neither the insulator-metal transition nor superconductivity are understood satisfactorily. Here, we undertake a first step in this direction by focussing on the pressure-driven insulator-metal transition using a combination of first- principles density-functional and many-body calculations. We report a striking result: the finding of an orbital-selective Mott transition in a pure p-band elemental system. We apply our theory to understand extant structural and transport data across the transition, and make a specific two-fluid prediction that is open to future test. Based thereupon, we propose a novel scenario where soft multiband modes built from microscopically coexisting itinerant and localized electronic states are natural candidates for the pairing glue in pressurized O2. The unique properties of high-pressure induced solid phases of molecular gases continue to evince keen and enduring interest in condensed matter physics. Beginning with early ideas of Mott1 and extending up to modern times2, ideas of pressure-induced electronic, magnetic and structural transitions and possible superconductivity in such systems even provided early ground for strongly correlated systems, are currently a frontline research topic in condensed matter. Particularly interesting examples of intriguing physics in solidized molecular phases 3 4, 5 of gases are dense hydrogen and solid oxygen , as well as the most recent report of very high-Tc superconduc- 6 tivity in solid H2S under very high pressure . H2 is predicted to metallize under high pressure, while solid O2 even shows a superconducting phase (Tc = 0.6 K) at the border of a pressure-driven transition from a non-magnetic insulator to paramagnetic metal, joining the long list of materials exhibiting superconductivity proximate to metal-insulator transitions. Pressurized molecular oxygen forms various low-temperature solid phases under pressure, labelled α, δ, ε and ζ phases7. At lower pressure, the antiferromagnetically ordered α phase transforms into another antiferromagnet- ically ordered δ phase at 5.4 GPa, followed by a non-magnetic ε phase at 8 GPa. Higher pressure, P 96 GPa, 8 9 metallizes the system , followed by emergence of superconductivity below Tc 06. K . This astounding behavior in a molecular system, reminiscent of strongly correlated, doped Mott insulators in d-band oxides like cuprates, presents a significant challenge for theory. The high-P ε–ζ phase transition is also accompanied by significant volume reduction10, with a contraction of about 10% of the lattice parameter along the b direction. The ε phase retains the layered nature of the lower pressure phases4, and the monoclinic (C2/m) structure10, 11 as shown in Fig. 1. That the driving force for the α–β transition at moderate T is dominantly magnetic has been established in a series of careful studies12–14. Indeed, early work of da Silva and Falicov15 already explained the measured heat of formation at the α–β transition in terms of the entropy difference computed from cluster analysis of a multi-orbital Hubbard model (or an equivalent S = 1 Heisenberg-like model in d = 2 dimensions). Observation of very different magnetic orders in the α, β phases, correlation between magnetic and structural changes along with ferromagnetic coupling between the off-plane near neighbors in theδ phase are reminiscent of those found in 16 classic multi-band systems like V2O3 , taken together with the above, favor a multi-orbital description. Additional 1Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, MT, Brazil. 2The Institute of Mathematical Sciences, C.I.T. Campus, Chennai, 600 113, India. 3School of Chemistry, Cardiff University, Cardiff, CF10 3AT, UK. Correspondence and requests for materials should be addressed to L.C. (email: [email protected]) SCIENTIFIC REPORTS | 7: 2632 | DOI:10.1038/s41598-017-02730-z 1 www.nature.com/scientificreports/ Figure 1. Crystal structure of the ε-phase of solid oxygen. The structure as viewed perpendicular to the a–b (a) and a–c (b) planes. The O8 clusters in the monoclinic unit cell (rose lines) are shown in (c). Ox(x = 1, 2, 3) label the three inequivalent oxygen atoms. evidence for multi-orbital effects is provided by the anisotropic and partially discontinuous pressure-induced changes in the lattice parameters in the different phases11, 17. In such a scenario, increasing pressure is expected, in the simplest approximation, to decrease lattice spacings and increase the carrier itinerance. The result would then be to suppress antiferromagnetic order along with insulating behavior, and to induce metalization. In solid 18 4 O2, antiferromagnetic order is destroyed well before metalization occurs , and so, within the p configuration of oxygen, the insulator-metal transition across the ε–ζ transition must be regarded as a Mott metal-insulator transition. This suggests that on the one extreme, a Heisenberg model description is only valid in the insulating α, β, δ phases, and that a more general multi-orbital Hubbard model must be used, at least for the ε phase. At the other extreme, one-electron band structure calculations for the antiferromagnetically ordered phases do provide qualitatively correct ground states19. In addition, electronic structure calculation based on generalized gradient approximation (GGA) shows that the nonmagnetic insulating state is energetically favored at pressures corre- sponding to the ε-phase20, 21. However, by construction, ab initio density-funtional calculations have intrinsic difficulties in describing non-magnetic insulating phases, and in particular theε phase22, 23, for reasons described in detail in ref. 24. The observation of superconductivity at the border of this (Mott) insulator-to-metal transition thus suggests that dualistic behavior of correlated carriers (see our discussion below) near the insulator-metal transition is very likely implicated in the pairing glue. Thus, a search for the microscopic origin of the pair glue must involve understanding of the insulator-metal transition around 96 GPa. Before presenting our local-density-approximation plus dynamical-mean-field (LDA + DMFT) results, we point out essential differences between band and Mott insulators. In conventional semiconductors (or band insu- lators) all bands below the Fermi energy are filled and, therefore, inert. Removing an electron leads to an empty state which can be thought of as a hole moving freely through the solid. The same is true for an added electron, which occupies the first empty band. In a multi-orbital Mott-Hubbard insulator, the insulating state arises because electron hopping from one site to another is inhibited by intra- and inter-orbital Coulomb repulsions. In these systems, when the band filling is slightly reduced from its commensurate value, a small number of unoccupied states are created; similarly adding electrons creates locally doubly occupied electronic states. The crucial differ- ence in this case is that since the doped carriers can have either spin (↑, ↓) with equal probability, doping a Mott insulator, e.g., by holes, creates two available states at the Fermi energy. This is at the heart of spectral weight transfer, a phenomenon ubiquitous to Mott, as opposed to band, insulators. In both cases, electron hopping might still be prevented by inter-orbital Coulomb interactions in a multiband system. The resulting metallic state upon doping can vary from a Fermi liquid at weak coupling to an exotic orbital-selective, non-Fermi liquid metal SCIENTIFIC REPORTS | 7: 2632 | DOI:10.1038/s41598-017-02730-z 2 www.nature.com/scientificreports/ Figure 2. Orbital resolved and total LDA density-of-states (DOS) for the three inequivalent oxygen atoms in the ε-phase. Notice that all bands as well span over the Fermi level. Also relevante is the evolution of the electronic DOS at different polarizations. for stronger electron-electron interactions, as doping and temperature25 are varied. This fundamental difference between band and multi-orbital Mott-Hubbard insulators is of basic and practical interest. Below we show that sizable multiband electronic interactions are the clue to the insulating state of the ε-phase of solid oxygen and its evolution to a non-Fermi liquid metallic state at high pressures. Possibility of Mott-Hubbard physics in purely p26–29 or s30 band systems is very intriguing, since the naive expectation dictates that the itinerance (kinetic energy of p, s-carriers) is appreciable compared to the electron-electron interactions, as distinct from d-band systems, where the d electrons reside in much narrower bands (hence the effective U/W is sizable; U and W are, respectively, the on-site Coulomb repulsion and the bare one-particle band width)31. Thus, understanding Mottness (or the proximity to a Mott-Hubbard insulating state) in materials with active p or s bands is undoubtedly an issue of great contemporary interest32. In light of the discussion above, we study how an orbital-selective interplay between appreciable p-band itinerance and sizable, on-site Coulomb repulsion, U, plays a central role in this unique Mott transition in solid O2. Results Electronic Structure. To quantify the correlated electronic structure of solid O2, we start with the C2/m structure (Fig. 1) with lattice parameters derived in ref. 11. Here, local-density approximation (LDA) calculations for the real crystal structure of the ε-phase were performed using the linear muffin-tin orbitals (LMTO)33–35 scheme in the atomic sphere approximation36.
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